One major drawback of the OFDM technique is inherent in the high fluctuations in the amplitude of the modulating signal obtained.
In the time domain, the summing of the independently modulated carriers is done coherently. Owing to the large number of these carriers that are summed together, amplitude extrema can be encountered in the modulating signal when the summing of the modulated carriers by the data symbols becomes constructive.
These extrema in the modulated symbol give rise to corresponding extrema in the modulated radiofrequency. In this case, it is not rare for the instantaneous power of the modulated signals to surpass the average power of the signal by more than 10 dB at certain points in time.
These large variations of amplitude and power cause problems in several respects:                first of all, they raise problems on the baseband modulating signal because they require over-sizing of the data path to enable the signal to propagate without clipping;        but above all they have consequences for the modulated radiofrequency signal because they need to have power stages sized to deliver instantaneous maximum peak power whereas it is only the average power of the signal that is of utility to ensure a link budget. The overconsumption associated with this special sizing of the transmission stages is a particular source of problems in systems using this type of multicarrier modulation.        
Different metrics are conventionally used to quantify these fluctuations. For example, the crest factor (CF) is often used for baseband modulating signals. Here, it is the ratio of the maximum amplitude of the signal to its root-mean-square (RMS) value. This ratio can itself be expressed in terms of natural value or decibels. For modulated radiofrequency signals, the PAPR (Peak to Average Power Ratio) is often used. This is then the ratio between the instantaneous power of the signal and its mean power, for a modulated signalx(t):
  PAPR  =                    max        t            ⁢                                              x            ⁡                          (              t              )                                                2                    E      ·              [                                                        x              ⁡                              (                t                )                                                          2                ]            
Here again, this ratio can be expressed in terms of natural value or decibels. Since this latter metric is based on the notion of the power of the modulated radiofrequency signal, it is often used in the radiofrequency domain because it is directly related to the problem of consumption of the power stages mentioned here above. In every case, there is a direct link between the extrema of the baseband modulating signal and the extrema of the modulated radiofrequency signal.
Faced with this problem of high-value extrema in this type of multicarrier modulation, different methods have been proposed to try and minimize them.
A first group of methods is based on what is known as “clipping” in which the amplitude of the signal is clipped when it goes beyond the pre-defined threshold. However, this clipping is by nature non-linear and introduces a distortion of the signal sent out that results not only in a degraded bit error rate but also a increase in the side lobes of the power spectral density of the signal after clipping.
A second group of methods is based on the application of a constraint or encoding on the data sequence emitted in order to limit the fluctuation of the modulating signal. In this method, a set of code words is built. This set of code words minimizes the extrema of this signal. Several techniques for building these codes have been proposed. The advantage of this approach is that it does not introduce any distortion. However, the spectral efficiency is penalized without even bringing any gain in encoding. In addition, to date, its field of application is limited to OFDM modulations with a small number of carriers because of its excessively high computational complexity.
In the face of these problems, a third group of methods has been proposed, based on the correction of constellation symbols modulating the carriers. The underlying idea in all these methods of this third group is that they play on the value of the modulation symbols to eliminate constructive summations during the coherent summing of all the carriers thus modulated. Several known methods are based on this principle, for example:                the “TI-CES” (Tone Injection Constellation Extension Scheme) methods as described for example in the article by S. H. Han, J. M. Cioffi, “Tone Injection with Hexagonal Constellation for Peak-to-Average Power Ratio Reduction in OFDM”, IEEE Communications Letters, Vol 10, no 9, September 2006, which proposes to increase the number of points of the constellation that modulate the OFDM carriers so that a point of the original constellation can have numerous corresponding possibilities of co-ordinates in the new constellation. According this approach, this additional degree of freedom is used to generate a signal of lower PAPR. However, the selection of the best possible co-ordinates for each point requires an increase in the computational complexity implemented, making it unsuited to hardware implementation for the real-time processing of signals.        the ACE (Active Constellation Extension) method, described for example in the article by B. S. Krongold, D. L. Jones, “PAR Reduction in OFDM via active Constellation Extension”, IEEE Trans. On Broadcasting, Vol. 49, no 3, September 2003, is also based on a constellation modification and relies on a shift towards greater distance from the decision axes. However, in the same way as for the preceding method, this technique is characterized by a very high computational complexity.        the “CD” (Constellation Distortion) method as described for example in the article by A. Aggarwal, E. R. Stauffer, T. H. Meng, “Computing the Optimal Amount of Constellation Distortion in OFDM Systems”, ICC 2007 Proceedings, is also based on a modification of constellations and relies on the hypothesis that the output level of the amplification of transmission is limited by instantaneous power peaks and that, if the amplitude of the peaks can be reduced, then the power emitted can be increased. According to this technique, for a given rate of distortion, a problem of optimization, known as a convex optimization problem, is resolved in order to elaborate an OFDM signal with a minimum global PAPR level. However, the computational complexity implemented increases exponentially when the constellation order becomes high.        the “TR” (Tone Reservation) method as described for example in the article by M. Mroué, A. Nafkha, J. Palicot, B. Gavalda, N. Dagorne “Performance and implementation Evaluation of TR PAPR Reduction Methods for DVB-T2”, International Journal of Digital Multimedia Broadcasting 2010, which proposes to reserve certain carriers of the OFDM multiplex that do not carry information but symbols optimized at emission to reduce the PAPR. These symbols can be optimized by using for example a convex optimization algorithm of the SOCP (Second Order Cone Programming) type. However, the computational power needed to implement this method remains great.        PCTS (Pre-Constructed Temporal Signal) described in the French patent application FR 3 003 107 which proposes to compute the symbol corrections on the basis of a complex correlation between, on the one hand, the cosine and sine samples of the carrier at a given order and, on the other hand, the real and imaginary samples of the peak values detected in the sum of the corrected carriers of an order lower or equal to the given order. Besides, the shifting of symbols authorized for the correction can be constrained and can correspond for example to the shifts permitted in the ACE method. However, here too, the computational complexity remains high when the number of carriers increases.        
It appears then that these methods for reducing extrema based on the correction of the constellation symbols modulating the carriers remain too complex in term of computation load when the number of carriers becomes great as is the case in modern broadcasting standards.
There is thus a need for a method for reducing extrema of an OFDM type multicarrier signal by correction of the constellation symbols that have limited complexity of implementation.